具有双时滞的企业竞争模型的稳定性分析
The Stability Analysis of the Enterprise Competition Model with Two Time Delays

以一类3维金融企业竞争模型为研究对象,研究时滞反馈作用下企业竞争的稳定性.首先,运用Hopf分支理论与稳定性得到系统正平衡点的特性; 其次,取时滞τ1和τ2作为分支参数,得到当经过分支点时,系统正平衡点的稳定性发生改变,继而引起混沌现象的消失,且可以分支出周期轨,也可以利用Hassard方法与中心流形定理,得到周期解的分支方向与稳定性的判定公式; 最后,利用Matlab数值模拟了时滞受控系统动力学行为随参数的演变,从而验证解析结果的有效性.
A three-dimensional financial enterprise competition model is made as the research object in this paper,and the stability of enterprise competition under the action of time-delay feedback is studied.Firstly,the positive equilibrium characteristics of the system are gotten on the basis of the theory of Hopf branch and stability.Secondly,taking time-delay τ1 and τ2 as branch parameters,the stability of the positive equilibrium point changes in the system when going through a branch point,which leads to the disappearance of the chaos phenomenon and can branch out of the cycle track.Similarly,the Hassard method and center manifold theorem are used to get the branch direction of periodic solution and judgment formula of stability.Finally,under the numerical simulation of Matlab,the dynamic behavior of the time-delay controlled system in the evolution of parameters is studied.Consequently,the validity of the analytical results is verified